Is COUNTDISTINCT base measure faster than calculated distinct measure? - ssas

Question

I have a fact table and dimension table that look like this
​Fact {DateKey,UserKey,ActionKey,Action Count}
I have a user dimension table that looks like this
DimUser {UserKey,Name,IsActive}
and a date dimension table that looks like this
DimDate { DateKey, Week, Year}
I have a physical distinct count measure on the DateKey column on the measure group based of the fact table..lets call it "DATE COUNT"
Now I want to have a calculated measure called "DAILY ACTIVE USERS" which will looks like this
[IsDailyActive] = IIF([Measures].[DATE COUNT] >= 21, 1, 0)
[Daily Active Users] = SUM([Dim User].[User Key].[User Key].Members, [Measures].[IsDailyActive])
There is also another way to solve this problem w/o using the physical distinct count measure as follows
[HasAction] = IIF([Measures].[Action Count] > 1, 1, 0)
[DATE COUNT] = SUM([Dim Date].[DATE KEY].[DATE KEY].Members, [Measures].[HasAction])
[IsDailyActive] = IIF([Measures].[DATE COUNT] >= 21, 1, 0)
[Daily Active Users] = SUM([Dim User].[User Key].[User Key].Members, [Measures].[IsDailyActive])
But I'm afraid the calculated measure will be slower than the physical distinct count measure that is calculated at processing time instead of at query time. Any thoughts of which will be better performing? My fact table has billion rows!